Equilibrium of non-neutral plasmas in a Malmberg–Penning trap with a weakly tilted magnetic field

The effect of small asymmetric magnetic perturbations on the equilibrium of a non-neutral plasma confined in a Malmberg-Penning trap is analyzed. A constraint, known in the theory of tandem mirrors as the condition of current closure, is derived for non-neutral plasmas. Together with Poisson's equation, this constraint provides a set of equations for determining self-consistent asymmetric equilibria of non-neutral plasmas in Malmberg-Penning traps. As an example of this approach, the non-neutral plasma equilibrium in the presence of a weak magnetic tilt is analyzed. Analytical and semianalytical solutions for the electric potential variations inside the trap are found in a paraxial limit for various radial density profiles of the plasma, including the case of global thermal equilibrium. The numerical procedure aimed to obtain self-consistent plasma equilibria for a magnetic field with a large asymmetry is also discussed. The newly developed method can be straightforwardly applied to determine plasma equilibria under the effect of the magnetic perturbations of higher multipolarity (such as, quadrupole or octupole fields).